David Dolžan

collaborators

5 papers

math.RA2026

Products of Nilpotent and Idempotent Matrices over Finite Local Rings

David Dolžan

Let $R$ be a finite commutative local principal ring. We study products of nilpotent and idempotent matrices in $M_{2} (R)$ . We show that every product of nilpotent and idempotent mat…

math.RA2026

Products of idempotents in a quaternion ring

David DolÅ¾an

Let $R$ be a finite commutative local principal ring, and let $H (R)$ denote the corresponding quaternion ring. We show that an element of $H (R)$ is a product of idempotents if and…

math.RA2026

Eigenvalues of the product matrices of finite commutative rings

David DolÅ¾an

The product matrix of a finite commutative ring $R = {x_{1}, x_{2}, \dots, x_{n}}$ and an element $u \in R$ is the matrix $A_{u} (R) = [a_{ij}]$ , where $a_{ij} = 1$ if $x_{i} x_{j} = u$ , and $a_{ij} = 0$ …

math.RA2025

Products of nilpotents in a quaternion ring of odd order

David DolÅ¾an

Let $R$ be a finite commutative local principal ring of cardinality $q^{n}$ , where $q = p^{r}$ for an odd prime $p$ and integer $r$ with $R / J (R) ≃ GF (q)$ . We determine the number…

math.RA2025

The multiplication probability of a finite ring

David DolÅ¾an

We study the probability that the product of two randomly chosen elements in a finite ring $R$ is equal to some fixed element $x \in R$ . We calculate this probability for semisimpl…